Jamal bought a 390 square inch poster. The length of the poster is 26 inches. What is the width, w, of the poster?

Given: A triangle ABC and a line DE parallel to BC.

To prove: A line parallel to one side of a triangle divides the other two sides proportionally.

Proof: Consider ΔABC and DE be the line parallel to Bc, then from ΔABC and ΔADE, we have

∠A=∠A (Common)

∠ADE=∠ABC (Corresponding angles)

Thus, by AA similarity, ΔABC is similar to ΔADE, therefore

AB/AD= AC/AE

⇒AD+DB/AD = AE+EC/AE

⇒1+DB/AD = 1+ EC/AE

⇒DB/AD = EC/AE

Therefore, a line parallel to one side of a triangle divides the other two sides proportionally.

⇒Therefore Proved

Hope this helps!!!